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# Calculus and Analysis

### Differential Functions : Values for Possible Solution

Determine for which values of m the function y(x)=x^m is a solution to the differential equation. 3x^2*y'' + 11x*y' - 3y = 0

### Find equation of the tangent line.

1) Find the equation to the tangent line y = tan x at x = 0

### Find Equation of a Line

See attached file for the problem.

### Working with limits.

See attached 1) F(x) = Is this continuous at x = 3?

### Differential: Determine dy/dx for Given Values

If dy/dx = 2y^2 and if y = -1 when x = 1, then when x = 2, y = ?

### Differential Equations : Free Fall and Terminal Velocity

An object in free fall in a gravitational field is governed by the ODE m*dv/dt=mg + Fs, where m is the mass of the object, g=9.8 meters/sec is the acceleration of gravity, v(t) is the velocity of the object t seconds after it is released, and Fs denotes external forces acting on the object. In all that follows, assume that v(0)

### Area of the Surface from Intersection of Two Cylinders

#22 Please see the attached file for full problem description.

### Chaos : Conjugacy in Discrete Dynamical Systems

I am taking a course in Dynamics/Chaos and I am trying to prove conjugacy between the logistic and quadratic functions. I have some ideas, but cannot get the proof to work. Attached is a word document with the functions and problem.

### Reflection in a Graph about the Origin

The graph of y=x^3 for x>=0 is given below. Complete the graph for x<0.

### Evaluating a simple limit

Evaluate Lt [(x2+5x+6)/(2x2-3x)] x→2

### Slope of a curve

Find the slope of the curve at point A in the graph.

### Slope of the line

Find the slope of the line in the graph.

### Estimating the limit of a function

Let y=f(x)=x^2+3 Find Limit of f(x) as x approaches 2 using both graph and table

### Intermediate value theorem

Define Intermediate-Value theorem Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1].

### Discontinuous function conditions

Define a discontinuous function and state the conditions for discontinuity. Find whether the following functions are discontinuous: f(x)=1/x and f(x)=(x)^(1/2) Solve the following:(involves jump discontinuity) A tomato wholesaler finds that the price of newly harvested tomatoes is \$16 per pound if he purchases fewer th

Find the radius of convergence of the series in the attached file 'Series.doc'.

### Implicit differentiation

If x^2+y^3=y+y^4, then find dy/dx

### Tangent through a point

A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north. the town of Coopers Crossing is situated on the river at its most northerly point. The town of Black Stump is 10 kilometres due south of Coopers Crossing. the town of And

### Recursive Equations : A 2x2xn hole in a wall is to be filled

Q.A 2x2xn hole in a wall is to be filled with 2n 1x1x2 bricks. In how many ways can this be done if the bricks are indistinguishable?

### Line Equations : Tangents & Normals

I) Find the equation of the tangent to y=x(1-x) at x=1 ii) Find the equation of the normal to y=x(1-x) at x=1 iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

### Differentiability and Limits

Please see the attached file for the fully formatted problems. Let f: I &#8594;&#8476; where I is an open interval containing the point c, and let k &#8712; &#8476;. Prove the following 1. f is differentiable at c with f &#8242;(x) = k iff lim h&#8594;0 [f(c+h) - f(c)]/h=k 2. If f is differentiable at c with f &#8242;(c) =

### Normalization constant of a Hermite polynomial

I need to figure out how to explicitly calculate the normalization facotor for the Hermite polynomial as it relates to the harmonic oscillator. N=[(a/Pi)1/2vv!]

### Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = x^2, y + z = 4, y = 0, z = 0

### Multivariable Calculus Functions

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = 10 - x^2 - y^2, y = x^2, x = y^2, z = 0

### Multivariable calculus

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you Sketch the solid bounded by the graphs of the given equation and find its volume by triple integration: z = y, y = x^2, y = 4, z = 0

### Multivariable Calculus : Radii of Gyration

Find the radii of gyration x and y( x and y have &#61657; above them) of the indicated lamina around the coordinate axes: The lamina of the region bounded by y = x^2 and y = 4; &#61540;(x, y) = y &#61540;: is the density symbol

### Multivariable Calculus: Mass and Centroid of a Plane Lamina

Find the mass and centroid of the plane lamina with the indicated shape and density: The region bounded by the parabolas y = x^2 and x = y^2, with &#61540;(x, y) = xy &#61540;: is the density symbol

### Multivariable Calculus : Centroid of a Plane

Find the centroid of the plane region bounded by the given curves. Assume that the density is &#61540; = 1 for each region: x = 0, y = 0, x + 2y = 4 &#61540;: is the density symbol

### Description of Multivariable Calculus: Volume of Solid of Revolution

Find the volume of the solid that is bounded above and below by the given surfaces z = z_1(x, y) and z = z_2(x, y) and lies above the plane region R bounded by the given curve r = g(u): z = 0, z = 3 + x + y; r = 2 sin u

### Multivariable Calculus : Double Integral - Polar Coordinates

Find the indicated area by double integration in polar coordinates: The area inside both the circles r = 1 and r = 2 sin u